When you install a new app in OS X, it usually comes in the form of a DMG file that you have to then mount, eject, and delete. This simple Automator service simplifies the process, ejecting the disk image and deleting its DMG file in one fell swoop.

Here's how to create this very simple service:

Open up the Automator application and select "Service".

Change the top two dropdown menus to receive "No Input" from the "Finder".

In the left sidebar, drag the "Run AppleScript" action into the right pane. Copy the following code into the box:

set my_selection to item 1 of selection_list
set my_kind to kind of my_selection
set my_name to name of my_selection

if my_kind is not "Volume" then
display dialog ¬
"Please select a volume mounted from a disk image file." with title ¬
"Selection is not a Disk Image" with icon stop ¬
buttons ["OK"] default button 1
return
end if

set match_found to false
repeat with v from 1 to (count volume_list)
if "/Volumes/" & my_name = item v of volume_list then
set match_found to true
exit repeat
end if
end repeat

if match_found is not equal to true then
display dialog ¬
"The selected volume does not appear to be a Disk Image." with title ¬
"Could not find Disk Image" with icon stop ¬
buttons ["OK"] default button 1
return
else
set my_source to POSIX file (item v of source_list) as alias
move my_source to the trash
eject my_selection
—reveal my_source
end if
end tell

Save the service as whatever you want (like "Eject & Delete DMG") and exit Automator.

Now, when you're done using a DMG file, you can just click on it, then go to Finder > Services > Eject & Delete DMG to eject the image and delete the DMG with one click. If you really want to make it fast, you can go to System Preferences > Keyboard > Keyboard Shortcuts and give your service a handy keyboard shortcut. Note that this doesn't work if you select the DMG in the Finder sidebar; you have to select it in an actual Finder window (or on the desktop). Hit the link to read more.